Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

Number of

$$\begin{array}{cc}\text { Line } & \text { Defective } \\ \text { Speed } & \begin{array}{c}\text { Dumber of } \\ \text { Parts Found }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

c. Use the least squares method to develop the estimated regression equation.

Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011 Hertz had 320,000 cars in service and annual revenue of approximately $\$ 4.2$ billion. The following data show the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies.$

$$\begin{array}{lcc}\text { Company } & \begin{array}{c}\text { Cars } \\ (\mathbf{1 0 0 0 s})\end{array} & \begin{array}{c}\text { Revenue } \\ \text{ (\$millions) }\end{array} \\ \text { U-Save Auto Rental System, Inc. } & 11.5 & 118 \\ \text { Payless Car Rental System, Inc. } & 10.0 & 135 \\ \text { ACE Rent A Car } & 9.0 & 100 \\ \text { Rent-A-Wreck of America } & 5.5 & 37 \\ \text { Triangle Rent-A-Car } & 4.2 & 40 \\ \text { Affordable/Sensible } & 3.3 & 32\end{array}$$

$

c. Use the least squares method to develop the estimated regression equation.

A program has a vector of structures that stores information on experimental data that has been collected. For each experiment, up to 10 data values were obtained. Each structure stores the number of data values for that experiment, and then the data values. The program is to calculate and print the average value for each experiment. Write a script to create some data in this format and print the averages.

Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011 Hertz had 320,000 cars in service and annual revenue of approximately $\$ 4.2$ billion. The following data show the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies.$

$$\begin{array}{lcc}\text { Company } & \begin{array}{c}\text { Cars } \\ (\mathbf{1 0 0 0 s})\end{array} & \begin{array}{c}\text { Revenue } \\ \text{ (\$millions) }\end{array} \\ \text { U-Save Auto Rental System, Inc. } & 11.5 & 118 \\ \text { Payless Car Rental System, Inc. } & 10.0 & 135 \\ \text { ACE Rent A Car } & 9.0 & 100 \\ \text { Rent-A-Wreck of America } & 5.5 & 37 \\ \text { Triangle Rent-A-Car } & 4.2 & 40 \\ \text { Affordable/Sensible } & 3.3 & 32\end{array}$$

$

a. Develop a scatter diagram with the number of cars in service as the independent variable.

The table shows the monthly revenue (in thousands of dollars) of a landscaping business for each month of the year 2013, with x = 1 representing January. A mathematical model that represents these data is f(x) =

$$\begin{cases} -1.97x + 26.3 \\ 0.505x^2 - 1.47x + 6.3\end{cases}$$

. How do the values obtained from the model compare with the actual data values?

Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011 Hertz had 320,000 cars in service and annual revenue of approximately $\$ 4.2$ billion. The following data show the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies.$

$$\begin{array}{lcc}\text { Company } & \begin{array}{c}\text { Cars } \\ (\mathbf{1 0 0 0 s})\end{array} & \begin{array}{c}\text { Revenue } \\ \text{ (\$millions) }\end{array} \\ \text { U-Save Auto Rental System, Inc. } & 11.5 & 118 \\ \text { Payless Car Rental System, Inc. } & 10.0 & 135 \\ \text { ACE Rent A Car } & 9.0 & 100 \\ \text { Rent-A-Wreck of America } & 5.5 & 37 \\ \text { Triangle Rent-A-Car } & 4.2 & 40 \\ \text { Affordable/Sensible } & 3.3 & 32\end{array}$$

$

d. For every additional car placed in service, estimate how much annual revenue will change.

Consumer Reports: Headphones. The following data show the brand, price (in dollars), and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports website). The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from $0$ (lowest) to $100$ (highest). The estimated regression equation for these data is $\hat{y}=23.194+.318 x$, where $x=$ price (in dollars) and $y=$ overall score.

$$\begin{array}{lcc}\text { Brand } & \text{ Price (\$) } & \text { Score } \\ \text { Bose } & 180 & 76 \\ \text { Skullcandy } & 150 & 71 \\ \text { Koss } & 95 & 61 \\ \text { Phillips/O'Neill } & 70 & 56 \\ \text { Denon } & 70 & 40 \\ \text { JVC } & 35 & 26\end{array}$$

What is the value of the sample correlation coefficient?

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \hline y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop the estimated regression equation for these data.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Use the least squares method to develop the estimated regression equation.

Use the least squares method to develop the estimated regression equation.

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

$$\begin{array}{|c|c|} \hline \text { Line } & \begin{array}{l} \text { Number of } \\ \text { Defective } \end{array} \\ \hline \text { Speed } & \text { Parts Found } \\ \hline 20 & 23 \\ \hline 20 & 21 \\ \hline 30 & 19 \\ \hline 30 & 16 \\ \hline 40 & 15 \\ \hline 40 & 17 \\ \hline 50 & 14 \\ \hline 50 & 11 \\ \hline \end{array}$$

a. Develop a scatter diagram with the line speed as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. Predict the number of defective parts found for a line speed of $25$ feet per minute.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Use the estimated regression equation to predict the value of y when x = 6.